Question
Expand the following \( 1.2 .1 \quad(a-2)\left(a^{2}\right. \) \( 1.2 .2-(2 x-5)^{2} \) 1.2 .3 \( \quad\left(\frac{a}{2}+1\right) \quad \) ?
Ask by Black Hammond. in South Africa
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Here are the expanded forms:
1. \( (a-2)(a^{2}) = a^{3} - 2a^{2} \)
2. \( -(2x-5)^{2} = -4x^{2} + 20x - 25 \)
3. \( \left(\frac{a}{2}+1\right) = \frac{a+2}{2} \)
Solution
Simplify the expression by following steps:
- step0: Add the terms:
\(\left(\frac{a}{2}+1\right)\)
- step1: Add the terms:
\(\frac{a+2}{2}\)
Expand the expression \( -(2 x-5)^{2} \)
Simplify the expression by following steps:
- step0: Evaluate the power:
\(-\left(2x-5\right)^{2}\)
- step1: Calculate:
\(-\left(4x^{2}-20x+25\right)\)
- step2: Calculate:
\(-4x^{2}+20x-25\)
Expand the expression \( (a-2)(a^{2}) \)
Simplify the expression by following steps:
- step0: Multiply the terms:
\(\left(a-2\right)\left(a^{2}\right)\)
- step1: Calculate:
\(\left(a-2\right)a^{2}\)
- step2: Multiply the terms:
\(a^{2}\left(a-2\right)\)
- step3: Apply the distributive property:
\(a^{2}\times a-a^{2}\times 2\)
- step4: Multiply the terms:
\(a^{3}-2a^{2}\)
Here are the expansions for each of the expressions:
1. **For \( (a-2)(a^{2}) \)**:
\[
(a-2)(a^{2}) = a^{3} - 2a^{2}
\]
2. **For \( -(2x-5)^{2} \)**:
\[
-(2x-5)^{2} = -4x^{2} + 20x - 25
\]
3. **For \( \left(\frac{a}{2}+1\right) \)**:
\[
\left(\frac{a}{2}+1\right) = \frac{a+2}{2}
\]
These are the expanded forms of the given expressions.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
Let's tackle these one by one! For the first expression \((a-2)a^2\), we distribute \(a^2\) to both terms in the parentheses, giving us \(a^3 - 2a^2\). Next, for the expression \(-(2x-5)^{2}\), we need to expand it. Using the formula \((b-c)^2 = b^2 - 2bc + c^2\), we have: \[ -(2x-5)^{2} = -((2x)^2 - 2 \cdot (2x) \cdot 5 + 5^2) = -(4x^2 - 20x + 25) = -4x^2 + 20x - 25. \] For \(\left(\frac{a}{2}+1\right)\), we'll distribute the terms by factoring out \(2\) to make it easier: \[ \frac{1}{2}a + 1. \] In summary, we have: 1. \(a^3 - 2a^2\) 2. \(-4x^2 + 20x - 25\) 3. \(\frac{1}{2}a + 1\)
